On the reductions of certain two-dimensional crystalline representations, III

Abstract

A conjecture of Breuil, Buzzard, and Emerton says that the slopes of certain reducible $p$-adic Galois representations must be integers. In previous work we showed this conjecture for representations that lie over certain non-subtle components of weight space. This article is a continuation of that work in which we also show the conjecture for the subtle components for slopes less than $\frac{p-1}{2}$.

Part III, previously was part of 1808.03224, should have some overlap with "On the reductions of certain two-dimensional crystalline representations, II". arXiv admin note: substantial text overlap with arXiv:1808.03224